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Question

If a pair of opposite angles of a quadrilateral are supplementary, the quadrilateral is:

A
cyclic
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B
parallelogram
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C
rectangle
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D
rhombus
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Solution

The correct option is C cyclic

Let ABCD be a cyclic quadrilateral.
Join OB and OD.
BOD=2BAD
BAD=12BOD
Similarly, BCD=12DOB
BAD+BCD=12BOD+12DOB
=12(BOD+DOB)

=12×360o
=180o.
A+C=180o
Similarly, B+D=180o.
If a pair of opposite angles of a quadrilateral are supplementary, the quadrilateral is a cyclic.


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